An arrangement for measuring the concentration of alcohol as a substance to be detected in breathing gas is disclosed in U. S. Pat. No. 4,770,026. In the known arrangement, a fuel cell is subjected to a gas sample having an alcohol vapor component and the physical measurement variable i(t), which is obtained by the electrochemical conversion, is supplied to an evaluation circuit which determines a measurement value proportional to the alcohol vapor concentration. The measurement value is determined by integrating the signal trace of the physical measurement value as a function of time (t). When the measuring cell is charged with alcohol vapor, the measurement signal first increases starting from a reference line, passes through a maximum value i.sub.max and returns again to a minimum value in the vicinity of the reference line after the complete electrochemical conversion. The area enclosed between the function value of the measurement signal and the reference line is proportional to the concentration of the alcohol vapor in the gas sample.
In the known measuring cell, the trace of the curve of the measurement signal changes with increasing deterioration of the measuring cell. Accordingly, the curve profile becomes flatter and wider in the course of the use time of the measuring cell. A similar change of the curve trace of the measurement signal occurs also after several measuring cycles occurring in rapid succession. This signal change is at least partially reversible after a longer recovery phase. For determining the concentration component of the alcohol vapor in the gas sample, integration takes place over the entire measurement signal trace. For this reason, the changes of the curve profile operate on the area content and therefore also on the measurement accuracy so that calibrating cycles must be repeatedly carried out with a gas sample of a known alcohol concentration. Calibration cycles of this kind make using the apparatus difficult especially when the measuring cell is subjected to gas at short time intervals. Furthermore, the composition of the substance to be detected must be known for the known evaluation method.